Why can't I set a rotation keyframe on this object without it setting the same keyframe on the parent armature? Deleting one KF deletes the other too
Turns out this was a case of user error. Bezier 1 was using the same action as the armature, and this is the normal behavior in that situation.
I was (incorrectly) thinking that an action just stores the entire timeline, including keyframes for each individual object that uses that action, because I hadn't had any problems using it that way with armatures. But in actuality, an action just stores the individual properties that are animated, and applies them to every object that performs the action, unless the object doesn't have that property. Which does make more sense in hindsight. I haven't had any problems using a single action for multiple armatures, but that's only because they don't have any bone names in common.